A different approach to logic

Abstract

The paper is about an approach to logic that differs from the standard first-order logic and otherknown approaches. It should be a new approach the author has created proposing to obtain a generaland unifying approach to logic and a faithful model of human mathematical deductive process. Welist the most relevant features of the system. In first-order logic there exist two different concepts ofterm and formula, in place of these two concepts in our approach we have just one notion ofexpression. The set-builder notation is enclosed as an expression-building pattern. In our system wecan easily express second-order and all-order conditions (the set to which a quantifier refers isexplicitly written in the expression). The meaning of a sentence will depend solely on the meaningof the symbols it contains, it will not depend on external ‘structures’. Our deductive system is basedon a very simple definition of proof and provides a good model of human mathematical deductiveprocess. The soundness and consistency of the system are proved, as well as the fact that our systemis not affected by the most known types of paradox. The paper provides both the theoreticalmaterial and two fully documented examples of deduction. The author believes his aims have beenachieved but obviously the reader is free to examine the system and get his own opinion about it.